GED Mathematical Reasoning TestQuantitative Problem Solving with Rational NumbersHard
A city's water reservoir has a capacity of 5.4 x 10^7 gallons. If the city uses 1.8 x 10^6 gallons of water per day, how many days will it take for the reservoir to be completely empty if it starts full?
- A30 days
- B3000 days
- C3 days
- D300 days
Show answer & explanationAnswer & explanation
Correct answer: A. 30 days
To find the number of days, divide the total capacity by the daily usage: (5.4 x 10^7) / (1.8 x 10^6). Divide the coefficients: 5.4 / 1.8 = 3. Subtract the exponents: 10^7 / 10^6 = 10^(7-6) = 10^1. Combine the results: 3 x 10^1 = 30 days.
Why the other options are wrong
- B. Incorrect. This would be the answer if the exponent difference was 3 (10^3).
- C. Incorrect. This would be the answer if the exponents were the same, or if 10^7 / 10^6 was 10^0.
- D. Incorrect. This would be the answer if the exponent difference was 2 (10^2).
Dividing Numbers in Scientific Notation
To divide numbers in scientific notation, divide their coefficients and subtract their exponents of 10. The result should be adjusted so the coefficient is between 1 and 10.
- Divide the numerical coefficients.
- Subtract the exponents of 10 (numerator exponent - denominator exponent).
- Combine the new coefficient and the new power of 10.
- Adjust the coefficient if it's not between 1 and 10, modifying the exponent accordingly.
Memory trick: Coefficients divide, exponents subtract, then check the form, that's a fact!